from Wiktionary, Creative Commons Attribution/Share-Alike License

Examples

Brown doesn't mention the "law of attraction" in The Lost Symbol but draws on noetic theory - which he calls noetic "science" - a realm of metaphysics that deals with forms of consciousness typically ignored by mainstream science.

In particular the book suffers from an ill-advised fling with something called noetic science, which explores the idea that human consciousness can affect the physical world, thereby providing (as we are reminded twice in the space of half a page) the

He called for more scientific research into the "the world of inner experience," meaning This new "noetic" science would eliminate the apparent contradiction between the experiential understanding of Hindu, Moslem, and Christian.

The remarks at the beginning of this post indicate that certain evangelical leaders were already adopting this worldview, and were even suggesting that theology needed to be reformulated to accommodate this "noetic" science.

Another example to add:
"Noetic refers to knowledge that comes to us directly through our subjective experiences or inner authority. This type of knowledge might take the form of an intuition that helps guide your decisions, or an epiphany that leads you to a creative breakthrough. Moreover, noetic experiences often carry an unusual level of authority that can help guide you to new understandings and new ways of being. Noetic experiences thus differ from the kind of knowledge that comes through reason or the objective study of the external world."
From p. 4 of Schlitz, M. M., Vieten, C., & Amorok, T. (2007). Living Deeply: The art & science of transformation in everyday life. New Harbringer Publications; Noetic Books: Oakland, CA.